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5.1.101 mult

Syntax:
mult ( ideal_expression )
mult ( module_expression )
Type:
int
Purpose:
computes the degree of the monomial ideal, resp. module, generated by the leading monomials of the input.
If the input is a standard basis of a homogeneous ideal then it returns the degree of this ideal.
If the input is a standard basis of an ideal in a (local) ring with respect to a local degree ordering then it returns the multiplicity of the ideal (in the sense of Samuel, with respect to the maximal ideal).
Example:
 
  ring r=32003,(x,y),ds;
  poly f=(x3+y5)^2+x2y7;
  ideal i=std(jacob(f));
  mult(i);
==> 46
  mult(std(f));
==> 6
See degree; dim; ideal; std; vdim.

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